An observer can see through a pin-hole the top end of a thin rod of height h, placed as shown in the figure. The beaker height is 3h and its radius h. When the beaker is filled with a liquid up to a height 2h, he can see the lower end of the rod. Then the refractive index of the liquid is

Options

A. `5//2`
B. `sqrt((5//2))`
C. `sqrt((3//2))`
D. `3//2`

Answer

B

Explanation

The line of sight of the observer remains constant, making an angle of `45^(@)` with the normal. `sintheta=(h)/(sqrt(h^(2)+(2h)^(2)))=(1)/(sqrt(5))`

`mu =(sin 45^(@))/(sin theta) = (1// sqrt(2))/(1 // sqrt(5)) = sqrt(((5)/(2)))`